Quiz #8
ECNS 303
Name________________________
1.) Suppose consumption is a linear function of disposable income:
C(Y-T) = a + b(Y-T),
Where a > 0 and 0 < b < 1. The parameter b is the marginal propensity to consume, and the
parameter a is a constant sometimes called autonomous consumption. Suppose also that
investment is a linear function of the interest rate:
I(r) = c – dr,
where c > 0 and d > 0. The parameter d measures the sensitivity of investment to the interest
rate, and the parameter c is a constant sometimes called autonomous investment.
a.) Solve for Y as a function of r, the exogenous variables G and T, and the model’s parameters
a, b, c and d.
Y = (a – bT + c - dr + G)/(1-b)
Suppose demand for real money balances is a linear function of income and the interest rate:
L(r, Y) = eY – fr,
where e > 0 and f > 0. The parameter e measures the sensitivity of money demand to income,
while the parameter f measures the sensitivity of money demand to the interest rate.
b.) Solve for r as a function of Y, M, and P and the parameters e and f.
r = (eY/f) – (M/fP)
c.) Use your answers to parts a.) and b.) to derive an expression for the aggregate demand curve.
Your expression should show Y as a function of P; of exogenous policy variables M, G, and T;
and the model’s parameters. This expression should not contain r.
Y = ((1/(e/f + (1-b)/d))((a-bT + c + G)/d + (M/fP))